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a, 15% of the commuters currently use the public transportation system, wh hs from now 10% of those who are now commuting to work via automobile nsportation will commute via automobile and 80% will continue to use public transition matrix for the Markov chain that describes the change in the mode A

a, 15% of the commuters currently use the public transportation system, wh hs from now 10% of those who are now commuting to work via automobile nsportation will commute via automobile and 80% will continue to use public transition matrix for the Markov chain that describes the change in the mode A

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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In a large metropolitan area, 15% of the commuters currently use the public transportation system, whereas the remaining 85% commute via automobile. The city has recently revitalized and expanded its public transportation system. It is expected that 6 months from now 10% of those who are now commuting to work via automobile will switch to public transportation, and 90% will continue to commute via automobile. At the same time, it is expected that 20% of those now using public transportation will commute via automobile and 80% will continue to use public transportation. (a) Construct the transition matrix for the Markov chain that describes the change in the mode of transportation used by these commuters. P T = A (b) Find the initial distribution vector for this Markov chain. Xo = (c) What percentage of the commuters are expected to use public transportation 6 months from now? (Round your answer to the nearest percent.)
Transcribed Image Text:In a large metropolitan area, 15% of the commuters currently use the public transportation system, whereas the remaining 85% commute via automobile. The city has recently revitalized and expanded its public transportation system. It is expected that 6 months from now 10% of those who are now commuting to work via automobile will switch to public transportation, and 90% will continue to commute via automobile. At the same time, it is expected that 20% of those now using public transportation will commute via automobile and 80% will continue to use public transportation. (a) Construct the transition matrix for the Markov chain that describes the change in the mode of transportation used by these commuters. P T = A (b) Find the initial distribution vector for this Markov chain. Xo = (c) What percentage of the commuters are expected to use public transportation 6 months from now? (Round your answer to the nearest percent.)
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